In the frequentist literature, introducing sparsity to the structure has been mostly done using regularization methods. [1]} and [2]} considered \(\ell _1\) -type penalty on the negative log-likelihood. They introduced sparsity to the structure of the model using sparse and shrinkage estimators. On the other hand, [3]}, [4]}, and [5]} considered thresholding method. However, the estimated covariance matrices from these methods sometimes contradicted with a positive definite constraint on covariance matrices. Other works in the frequentist context include banding and tapering, e.g., [6]}, [7]}, and [8]}. Their estimators are often used for Gaussian covariance graph model and are well supported by the asymptotic statistical properties.
